Question

An A.P. 5,12,19,....has 50 terms. Find its last term and hence find the sum of its terms .

Answer 1

Given,

$a=5,d=12-5=7,n=50$

Last term,

$a_n=a+(n-1)d$

$=5+(50-1)7=348$

$S_n=\frac{n}{2}[2a+(n-1\left)d\right]$

$=\frac{50}{2}\left[2\right(5)+(50-1\left)7\right]$

$=25[10+49\times 7]$

$=8825$